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1
2 ... ( ).,.,..,.,
3 1.,.,., (F ederal F und Rate) %p, %. IMF.,.
4 . 3.,,,. (determ inistic approach ) (stochastic approach ).,, (ruin probability ).,,. (M oody ' s ),.,.
5 4.. (low er bound),,. 4. (stochastic process m odel). (lognorm al m odel), Jetton, CIR. Jetton, CIR (increm ent ), Jetton CIR (m ean rev erting property ).
6 , ( ).,.,,, Jetton 9.00% 7.73% f(t) CIR , CIR % ( : ). t=1 t=2 t=3 t=4 t=5 41,063 57,684 69,837 83,333 92,804 Jetton 41,063 56,761 67,245 77,252 82,552 CIR 39,196 53,624 62,856 72,246 77,773,..
7 ,,,,.,,,., Jetton, CIR, Jetton.,,.,,,.
8
9 < - 1> 8 < - 2> 9 < - 3> 11 < - 4> 12 < - 5> 13 < - 1> 23 < - 2> 27 < - 3> 28 < - 4> 29 < - 5> 31 < - 1> 34 < - 2> 38 < - 3> 57 < - 4> 58 < - 5> 60 < - 6> 62 < - 7> 63 < - 8> 64 < - 9> 65
10 < - 1> 5 < - 2> 5 < - 3> 6 < - 1> 35 < - 2> 37 < - 3> 39 < - 4> 41 < - 5> 43 < - 6> 44 < - 7> 46 < - 8> 49 < - 9> Jetton 50 < - 10> 53 < - 11> 56 < - 12> 58 < - 13> 59 < - 14> 68 < - 15> 69
11 1. 1. IMF,. 1)..,., (lock in ),..,, (assum ed interest rate risk ). 1) ,.
12 2. (RBC),,. 3., Jetton, CIR ,, 2.,
13 3 3.,
14 )., (F ederal F und Rate) % 6.0% 1 5.5% 0.5%p 1%p 16 3).., FF, CD, T - Bill(3M ), T - Bill(1YR ), T - Bond (10YR ) % 2001 (< - 1> ) F F, CD (90 ) 5.49%, 5.26% T - Bond(10YR) 5.10%, T - Bill(3M ) T - Bill(1YR) 4% 4.88%, 4.51%. 2) %p, %p, %p, %p. 3), " ",, 611, LG,
15 5. < - 1>.,, (< - 2> ). < - 2> Call(1 ), CD (90 ), (5 ) Call(1 ) CD %, (5 ) 0%
16 6. 0% < - 2>.. Call(1 ), CD (90 ), (5 ), (1 ), Call(1 ) %, CD (90 ) 25.00%, %. IMF 6% 10%, Call(1 ), CD (90 ), (1 ) 5.05%, 5.68%, 5.65%, % 11 6%. < - 3>
17 7 IMF (< - 3> ).,.,.. 2.., F Y ' F Y ' %p. FY '99 2%p.,., FY '87 7.5%p FY ' %p. FY ' % 7.5% ( ) 0.4%p
18 8 (< - 1> ). < - 1> ( : %) '82 '87 '92 '94 '98 ' : '00 3/ %., 4)..., A BBB... 4) , % 16 1,592 (, ).
19 %, FY ' 98 (< - 2> ). < - 2> ( : %) FY ' ' ' ' ' ' ' ' ' ' ' ,,, %...
20 10..,.. (duration ).. < - 3> F Y ' % FY ' % 1.7%p, F Y ' % FY ' %p. FY ' % F Y ' %. F Y ' % 0%
21 11 < - 3> FY 92 FY 96 FY'00 ( : %) (a) (b) (a-b) NA : 1. 3, 1, ( : ) , ) FY ' 94 FY ' ,, (< - 4> ).
22 12, (cash flow underw riting ). < - 4> ( : %) FY'94 FY'95 FY'96 FY'97 FY'98 FY'99 FY' : FY ' , FY % FY ' %.,,, 72.4%, 74.0% 1.6%.,,.,,
23 13. (interest rate risk ) (insurance risk ). (duration m atching ). (law of large num ber ), ALM. 2). 6 7%. < - 5> ( : %) 7.5% 8.5% : 6. < - 5>,,
24 14. < - 5> FY ' %, FY ' % 70%. 7.8% 8.0% 5), 8.3% 8.5%.. F Y ' %, F Y ' %,.,,. 5)
25 (long term ). (equivalence principle) (present value). (discount rate).. 3,,,.,...
26 16...,,,,.. 6) 1) 7),. 8). 6) (1996b), (1996) (1999). Ogawa, H amori and Ohno(1997), (2000).. 7), " ",,,
27 17. 9).,. 2),.,..,.. 8). 9).
28 18 3) 10),.., (call option ).,,. 11).,. 12). 10),,, ). 12),.
29 19 2., (m acro).. 13) 1), (base)., 14)., ( ).. 13). 14) (NAIC Standard Valuation Law), (Calender Year Statutory Valuation Interest Rate) (base).
30 20, (sw ap )., 15). 2) ( ) + = Fisher.., 16),, F isher ( ) 17).. (building block approach ) 18). 15). 16), =. 17) Abel, A. B., "Assessing Dynamic Efficiency: Theory and Evidence", Review of Economic Studies, ).
31 21. 19) 1) (m ean - variance approach ) X ( ) ( 2 ). X, r P (X< r ), E {m ax (r - X, 0)}, r - +.,. 2) Option. (cost ) (put option ). (hedge) (arbitrage)., 19)..
32 22 (volatility ). 3) (ruin probability ). ( ) (cash flow ), 20),. (M onte Carlo m ethod) 21),., 22).. < - 1>. 20),. 21) (random number),.. 22) Wilkie..
33 23,,.. < - 1> ( ) ( ) ( ) / Fisher + = < > - - -
34 ),.,,,.,...,...,,.
35 25.. 2),.. (2. 5% 3.0% ), % : I = 3% + W ( R 1-3% ) + W 2 ( R 2-9% ) : I = 3% + W ( R - 3% ) I, R (reference interest rate), R 1 =Min (R, 9% ), R 2 =Max (R, 9% ) W (w eighting factor ).. (9.0% )
36 26. M oody ( Y 12 ) 36 ( Y 36 ).. 10 : M in ( Y 12, Y 36 ) 10 : Y 12. 3) < - 2> %, (Single Prem ium Deffered Annuity ) %, 7.00%.,, < - 3> %, % 125%
37 27 23). < - 2> % 6.25% 7.75% % 5.75% 7.00% % 6.50% % 6.00% 7.25% % 6.75% % 6.25% % 7.00% 2001 NA NA : Prescribed Statutory and T ax Interest Rates for the Valuation of Life Insurance and Annuity Products, T illinghast- T ow ers Perrin, %, 5.00% %, 10.19% 4.00%.. 1) 1996, 23) 4.50% 4.50% 125% 5.625%.
38 28.. < - 3> % 6.76% 8.06% % 6.89% 7.96% % 7.07% 7.99% % 7.05% 7.98% % 7.32% 8.41% % 7.62% 8.05% % 6.84% 7.57% % 6.83% 7.77% % 6.75% 7.78% % 6.77% 7.93% % 6.87% 7.73% % 6.72% 7.87% - : ,..,, ( ) ( ). 2)
39 % 20%. = ( % ) (0.8% ) 0.2 = % %, 80%. 10. < - 4> ) 25). ( : ). < - 4> (1- ) : 10 ( 1996 ) 24). 25) FY' % %.
40 30.. (Gilt s ),,,,., 3 4%..,, 6% +( 6% 1/ 4), 7.5% %, 7.5% %, 6.5% 1%p. 1. 1, ( ),,
41 (< - 5> )... < -5> (A) (B) 5.5% 6.5% A-0.5%, A-1.0% A-1.5%, A-2.0% ( , ) B 120%. 26)27) 26) ) 115 ( ). 1. ( ) 2. ( ).,.,
42 32 28) 29)., F Y ' % 7.5% 30). 9% 6.5%. 6.5%., ). 29) ) 78 1
43 (actuarial view of risk ) C (C risks ) 31) C- 1 (as set risk ), C- 2 (pricing risk ), C- 3 (interest rate risk ), C- 4 (general m anagem ent risk, miscellaneous risk ) 32) (< - 1> ) 33). C,. (C- 2) (as sum ed rate) 34) 35). 31) Contingency risks. 32),,,. 33) Santomero & Babbel (financial view of risk) (actuarial risk), (systematic risk), (credit risk), (liquidity risk), (operational risk), (legal risk). Financial Risk Managements by Insurers, pp ) (adequate), (reasonable),
44 34 (< - 1> ).. < - 1> C-1 ( ) C-2 ( ) C-3 ( ) C-4 ( ) o (, ) o o, (mortality, morbidity),, o o o (Asset Liability mismatching) o (, ) o, o,, : 1. Conant, S. et al, Managing for Solvency and Probability in Life (equitable). 35) (, RBC ( ) - Risk Based Capital Formula -,, 1993). (, ),,,.,, " "
45 35 and Health Insurance Companies, LOMA, pp Black, K. (1994), pp ,,,.,. < - 1> : Black, K. (1994), p.854.,... 36).
46 )..,.,...,,. 36). 37) (demography),. (underwriting)..
47 37, (low er bound) 38)., (< - 2> ). < - 2>.,, (positiv e)., (positive), 38), " Solvency margin ( ) ", 1994., " Risk,,
48 38. n, m a,. n a = 1 m a b = 1 max ( 0, ab - a ) ab, < - 2>. < - 2> i 1 % i 2 % i k % i k + 1% i m a % R 1 R 2 R k R k + 1 R m a = k j = 1 ( i j - i ML ) R j : (im L ) ik ik (m inimum ) p (p percentile),.
49 39 (param etric m ethod) (statistical distribution ) (confidence interval)...,. 2..., 4 (< - 3> ). < - 3> /,
50 40 (interest rate generation m odel) 39),.,.,..,., (scenario) 40)., RBC. 41),. 39),. 40) (interest rate path). 41), Cash Flow Testing,, 1998, pp
51 41
52 42...,. (pricing m odel), (prediction m odel), (risk analy sis m odel) (< - 4> ). < - 4> 42) (interest - rate- derivative securities ) (trading securities ) (derivative securities )., (point estim ation ). 42) (no- arbitrage model) (equilibrium model). T uckman (1996), pp
53 43 (professional judgm ent and experience). (multiple tim e periods ) 43),, ALM (as set liability m anagem ent ).. (arbitrary m odel), (lattice m odel), (stochastic process m odel) (< - 5> ). 1) (non - stochastic m odel), 44). (optimistic case), (pessimistic case) (m idrange ca se)., (depression ) (hyperinflation ). 43) (month), (quarter), (annual). 44) (deterministic model) (preset model).
54 44. (sensitivity analy sis ), (stress testing ), 126 (New York Regulation 126) 7 45) (< - 5> ). < - 5> 2) 46). (binom ial lattice m odel) (lattice) 47) 45), %p, 0.5%p, 5 1.0%p 5 1.0%p, 5 1.0%p 5 1.0%p, 3.0%p, 3.0%p.. 46) (tree model) (probabilistic model). 47) (decision tree).
55 45, (< - 6> ). < - 6> r 4 r 3 r 2 r 1 r 0 r - 1 r - 2 r - 3 r - 4 t 0 t 1 t2 t3 t 4 : r t (1) (- 1). (con stant ),. (constant ) c k, (1) (2) 48). ( ) r k = r 0 + c k, k = 0, 1, 2, (1) ( ) r k = r 0 ( 1 + c) k, k = 0, 1, 2, (2) ) Jetton (1988).
56 46.., (m ultinomial lattice)., (upper bound) (low er bound),. 3) (param eter ) (W iener process ). 49) 50). < - 7>. 49) (volatility) (drift). 50), (correction factor mean reverting factor),.
57 47 < - 7> : 7.0%, 0.3, 100 Vasicek (1977) 51) Cox, Inger soll Ross (1985) 52), Ho Lee (1986) 53), Black, Derm an T oy (1990) 54), H eath, Jarrow M orton (1990) 55), Black Karasin ski(1991) 56), (short - rate). (lognorm al 51) Vasicek, O., "An Equilibrium Characterization of the Term Structure", Journal of Financial Economics, Vol. 5, ) Cox, J. C., Ingersoll, J. E. and Ross, S. A.(1985). 53) H o, T.S.Y. and Lee, S. B., "Term Structure Movements and Pricing Interest Rate Contingent Claim s", The Journal of Finance, Vol. XLI, ) Black, F., Derm an, E. and Toy, W., "A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options", Fiancial A nalysts Journal, Vol. 46, ) Heath, D., Jarrow, R. and Morton, A., "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approxim ation", Journal of Financial and Quantitative A nalysis, Vol. 25, ) Black, F. and Karasinski, P., "Bond and Option Pricing When Short Rates are Lognorm al", Financial A nalysts Journal, Vol. 46, 1991.
58 48 m odel) 57), CIR, Jetton 58), Stromm en 59), Gur ski 60), M ereu 61) 62). ) 63). (random shock ),, log ( r t + 1 / r t ) 64) t 2 t (norm al distribution ). (3), Z (standard norm al distribution ) 65). t (drift ) t t. log r t + 1 r t = t + t Z (3) ( 3). log r t + 1 r t = log ( 1 + r t r t r t ) = log ( 1 + r t r t ) 57) Tuckman(1996), pp ) Jetton (1988). 59) Strommen, S., Discu ssion of Jetton(1988). 60) Gurski, J. M., Discussion of Jetton(1988). 61) Mereu (1990). 62) Christiansen(1992). 63) 1980 (Salomon Brothers Model). 64) (natural logarithm). 65) 0, 1., Z N (0,1).
59 (4) x log (1+x ) log (x ) (4) (5). log r t + 1 r t r t r t (5) (3) (5) (discrete stochastic process ) (stochastic differential equation ) (6). (6) dw (standard W iener process ) 66). d r t r t = t d t + t d W (6) (6) t 0 t (con stant ), t t =. r t + 1 = r t e Z (7) (negative),. 66) (Brownian Motion) (increment) (stationary), (variance proportional to the time interval) (diffusion process). 1.
60 50.. n, (7) (8). r t + n = r t e n Z (8)
61 51 ) Jetton.,. (m ean rev ersion ). (m ean rever sionary process ),. (long - run m ean rate, r ) 67).,, (< - 8> ). < - 8> r t r t Jetton (1988) (before type). 67) (target rate).
62 52 r t + 1 = [ r t + f ( t ) ] e Z (9) (9) 1 (T reasury bond), (9) 0.27, f ( t ). f ( t ) = r t < r min [ r - r t ] 3, 0.5 [ r - r t ] r t > r max [ r - r t ] 3, 0.5 [ r - r t ] r 1, r 0 r 0. < - 9> Jetton : = r - r t < - 8> 68), Jetton 69) 68) (the speed of the interest rate to its long-run mean). 69)
63 53 (ab solute v alue) 5.77, 3 (< - 9> ). Jetton t. ) CIR Jetton. Cox (1985) CIR (increm ent ). (diffu sion process ) 70). dw. d r = ( r, t ) d t + ( r, t ) d W (10) CIR (m ean rev erting stocha stic process ),. d r = a ( - r ) d t + r d W (11) r, a,, dw. (11) (12) CIR. Z N (0,1).. 70) (drift term) (diffusion term) (continuous time Markov process),.
64 54 r = a ( - r ) t + r Z (12) (deterministic com ponent, ) (stochastic component, ) CIR 71)., 72) (negative).,.., Jetton, CIR. (13) (14) 73). d r = ( r ) d t + ( r ) d W (13) d r r = ( r ) d t + ( r ) d W (14).. Jetton CIR.. 71) Cox (1985). 72) (square root). 73) t.
65 55 Jetton CIR. r Z, Jetton 1, CIR ). 74) Chan et al.(1991). Chan, K. C et al., "The Volatility of Short-Term Interest Rates: An Empirical Comparison of Alternative Models of the Term Structure of Interest Rates", Working Paper, The A cademy Faculty of Finance, Ohio State University, Rebonato(1996) p.239.
66 56 3.., ( "A " ) A. A < - 10> 75%, 25%. < - 10> : %..., 8 9%.
67 57,., 1 75) 3 76)..,,,..,,,.,, A 77). 75),,,. 76) (1998) p.70.
68 58. 1) ) 5,, Jetton CIR 79) , (< - 11> ). Jetton [f (t )], CIR ) )... 78) ). 80).
69 59 81) 82). < - 11> : w ww.bok.or.kr. (norm ality ), 83). Jetton CIR 84) < - 3>. 81). 82) Jetton CIR,. 83) Shapiro-Wilk p-value p-value. 84) CIR (regression analysis) (maximum likelihood estimation method).
70 60 < - 3> Jetton 9.00% 7.73% f(t) CIR : f(t) Jetton. 2) < - 3> 5. 85) (random num ber generation )., Jetton, CIR 2,000, A..,, % 86) A (< - 12> ). 85). 86).
71 61 < - 12> : Jetton t=1. 90% < - 3>, Jetton, CIR 2000, A < - 4>. < - 4> ( : ) t=1 t=2 t=3 t=4 t=5 41,063 57,684 69,837 83,333 92,804 Jetton 41,063 56,761 67,245 77,252 82,552 CIR 39,196 53,624 62,856 72,246 77,773 A 1 41,063, 2 57,684, 3 69,837. A A. 3) < - 13>
72 62,.. < - 13>. Jetton CIR..,. Jetton CIR CIR Jetton 95%. Jetton CIR Jetton CIR.
73 63. 4) 87) A 75%, 25% % 36 37% (< - 5> ). < - 5> ( : %) t=1 t=2 t=3 t=4 t=5 64.1/ / / / / 36.8 Jetton 64.1/ / / / / 38.1 CIR 62.5/ / / / / 39.7 : /, A, A.. 87),.
74 64., 88). < - 5>,. Jetton CIR. A,. 5) A. A,.,. A. A A 95%, 90% 88),.
75 65 < - 6>. < - 6> ( : %) t=1 t=2 t=3 t=4 t= % Jetton CIR % Jetton CIR : 100%.,. 95% 70 85%, 90% 40 70%. CIR. < - 7>,. < - 7> ( : %)
76 66 100% 95% 90% : 100%. A,. < - 10> 8 9%. 4..,,,,..,,,,.
77 67,.,,, (1998),,,, (3 ) (< - 8> ) 89). < - 8> : (1998), p69., (1998), (< - 9> ).,,,. 89),..
78 68. 90) (< - 9> ). < - 9> : 1 : ,,,,..,.. 90) (coefficient of variation).
79 69, Jetton, CIR 91). 92).,,,. Christiansen (1992) 93), Jetton CIR.,.,., 91). 92) NAIC (Cash Flow Scenario Testing). http :/ / 1products/ finance lrbc3/. 93) Christiansen(1992) 126 (New York Regulation 126), (reasonable),,, (volatility).
80 70 (Canadian In stitute of Actuaries ) 1,000 94). (confidence lev el). 95).. 1) 5.5%, 6.5% , 50% 7 8% 9% 7% (< - 14> ).. < - 14> 94) Britt(2000). 95) 90% 2,
81 71 : ). 97),. 98)..,,. 96) (arc tangent). 97) 13 FY' %, FY' %, FY %. 98), (Survival Analysis),, , pp
82 72 2), ( 65% ) 30 60% (< - 15> ).,. < - 15> : ,, 99),
83 73..,,,.. 99) (moving average).
84 74.,.,,.,.,....,. 100). 100), RBC 11.2% 11.8%. < > % 11.9% 11.8% 11.3%
85 75,.,.,.,.,., (ca sh flow analy sis ), ,. (tool)..,. 101). 101),
86 76..
87 77, " ",,, , " ",,, ,,,, , " ".,, , " ",, , " ",, ,,.,,, 1999.,, 98-8,, 1998.,,,, ,,, Atkin son and Dallas, Life In surance Products and Finance, Society of A ctuaries, Black, K. and Skipper, H. D., Life In surance, Prentice- Hall International, Inc., 3rd E dition, Britt, S. et al., "E conomic S cenarios Generators", 2000 Valuation A ctuary Symposium W a shington, D.C., Sept Byrne, F. and Cumm ing s, T. M., "M anaging Interest Rate Risk ",
88 78 E mp has is, T illinghast - T ow er s Perrin, Christiansen, S. L., "A Practical Guide to Interest Rate Generator s for C- 3 Risk Analy sis", T ransactions of S ociety of A ctuaries, Vol. XLIV, Cox, J. C., Ingersoll, J. E. and Ross, S. A., "A T heory of the T erm Structure of Interest Rates", E conom etrica, Vol. 53, Jetton, M. F., "Interest Rate Scenarios ", T ransactions of S ocie ty of A ctuaries, Vol. XL, Kellison, S. G., T he T hoery of Interest, Richard D. Irwin, Inc., M ereu, J. A., "A Guide to Quantifying C- 3 Risk", T ransactions of S ocie ty of A ctuaries, Vol. XLI, Rebonato, R., Interest - Rate Option M odels, John W iley & Son s, Sherris, M., "A One- F actor Interest Rate M odel and the Valuation of Loans w ith Prepaym ent Provision s", T ransactions of S ocie ty of A ctuaries, Vol. XLVI, Sherris, M. and Ang, A., "Interest Rate Risk M anagem ent : Developm ents in Interest Rate T erm Structure M odeling for Risk M anagem ent and Valuation of Interest - Rate- Dependent Cash Flow s", N orth A m erican A ctuarial J ournal, Vol. 1, T uckm an, B., Fixed Incom e S ecurities, John W iley & S on s, Inc., 1996.,,, ,,,
89 79, " ",, , " ",,, 63 2,
90 96-1 / /, , : /,, /, /, /, (I) : /, : /, /, /, : /, M&A : M&A /, / , /, ( ) : /, /, : /,
91 98-7 /, /, ( ) : /, /, : /, /,, (Survival Analysis) /, : /, /, /, / ART /, /, /, /, /, / /, /, /, /, OECD /, /,
92 /, /, /, , /, /, /, (IIS) ( 33 ), (PIC) ( 18 ), ( I ) /, /, /, M&A /, MAI /, /,,, ( ) : /, ( ) : /, /, /, /, : /, /, : /, /,
93 99-9 (Underwriting) / /, /, /, /, /, /, /, /, '98, '99, : /, /, CEO Report 1 /, ( ) 2 /, ( ) 3 /, /, Insurance Business Report 1, OECD /, /, /, IMF /,
94 6 /, /, :,,, /, (IT) : /, /, IMF /, /, /, Environment Changes in the Korean Insurance Industry in Recent Years : Institutional Improvement, Deregulation and Liberalization / Hokyung Kim, Sangho Park, Korean Insurance Industry 2000 / Insurance Research Center,
95 ,,,,,, (e- mail: ) (e- mail: dslee@kidi.or.kr ) ( ) ISBN ,000
ๆญฏ์ฐ๋ณด01-04.PDF
36. 1. IN G 8 ) ING,.... ING.,,,,. (Executive Board) (Risk Policy Com mittee), (Central Credit Comm ittee), (Central Limit s Com mittee).,,.,. 8) 1999 ING Annual Report pp. 32 36 pp. 94 95. 37 1) ING,
์๋์ง๊ฒฝ์ ์ฐ๊ตฌ Korean Energy Economic Review Volume 11, Number 2, September 2012 : pp. 1~26 ์ค๋ฌผ์ต์ ์์ด์ฉํํด์ํ๋ ฅ์ค์ฆ๋จ์ง ์ฌ์ ์๊ฒฝ์ ์ฑํ๊ฐ 1
์๋์ง๊ฒฝ์ ์ฐ๊ตฌ Korean Energy Economic Review Volume 11, Number 2, September 2012 : pp. 1~26 ์ค๋ฌผ์ต์
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๊ธฐํ์๋ฃ.PDF
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The e-business Studies Volume 17, Number 6, December, 30, 2016:275~289 Received: 2016/12/02, Accepted: 2016/12/22 Revised: 2016/12/20, Published: 2016/12/30 [ABSTRACT] SNS is used in various fields. Although
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